A cylindrical shaft of diameter ‘D’ rotates about a vertical axis inside a fixed cylindrical tube of length ‘L’ and a very thin gap of ‘h’ between shaft and tube. If the space between the shaft and tube is filled by a lubricant of dynamic viscosity ‘µ’. Then determine the power required to overcome viscous resistance when the shaft is rotated at a speed of ‘w’.
1
\(\pi^2\mu^2D^3Lw^3\over8h\)
2
\(\pi\mu D^3Lw^2\over4h\)
3
\(\pi\mu D^4L^2w\over16h^2\)
4
\(\pi\mu^2D^2L^2w^2\over2h\)